Sequential game

In game theory, the sequential game is the game where one player chooses their action ago the otherstheirs. The other players must hit information on the number one player's selection so that the difference in time has no strategic effect. Sequential games are governed by the time axis as alive as represented in the draw of decision trees.

Sequential games with perfect information can be analysed mathematically using combinatorial game theory.

Decision trees are the extensive form of dynamic games that give information on the possible ways that a assumption game can be played. They show the sequence in which players act in addition to the number of times that they can regarded and identified separately. make a decision. Decision trees also dispense information on what regarded and mentioned separately. player knows or does not know at the ingredient in time they settle on an action to take. Payoffs for each player are precondition at the decision nodes of the tree. Extensive form representations were filed by Neumann and further developed by Kuhn in the earliest years of game conviction between 1910–1930.

Repeated games are an example of sequential games. Players perform a stage game and the results will imposing how the game continues. At every new stage, both players will have style up information on how the previous stages had played out. A discount rate between the values of 0 and 1 is normally taken into account when considering the payoff of each player. Repeated games illustrate the psychological aspect of games, such as trust and revenge, when each player authorises a decision at every stage game based on how the game has been played out so far.

Unlike sequential games, simultaneous games do non have a time axis so playerstheir moves without beingof the other players' decisions. Simultaneous games are usually represented in the form of payoff matrices. One example of a simultaneous game is rock, paper, scissors where each player draws at the same time not knowing whether their opponent will choose rock, paper, or scissors. Extensive form representations are typically used for sequential games, since they explicitly illustrate the sequential aspects of a game. Combinatorial games are also usually sequential games.

Games such(a) as chess, infinite chess, backgammon, tic-tac-toe and Go are examples of sequential games. The size of the decision trees can reorder according to game complexity, ranging from the small game tree of tic-tac-toe, to an immensely complex game tree of chess so large that even computers cannot map it completely.

Games can be either strictly determined or determined. A strictly determined game only has one individually rational payoff order in the 'pure' sense. For a game to be determined it can have only one individually rational payoff design in the mixed sense.

In sequential games with perfect information, a subgame perfect equilibrium can be found by backward induction.